QQuestion
When two conductors are connected in series, the equivalent resistance is 25 Ω, and when connected in parallel, the equivalent resistance is 6 Ω. Determine the resistance of each conductor.
✓Answer
Let the resistances be R₁ and R₂.
For series combination:
R₁ + R₂ = 25 Ω …(1)
For parallel combination: 6 = \frac{\text{R₁R₂}}{\text{R₁}+\text{R₂}}
Using (1),
6 = \frac{\text{R₁R₂}}{25}
Therefore,
R₁R₂ = 150 …(2)
From (1), R₂ = 25 − R₁
Putting in (2), R₁(25 − R₁) = 150
25R₁ − R₁² = 150
⇒ R₁² − 25R₁ + 150 = 0
⇒ R₁² − 15R₁ − 10R₁ + 150 = 0
⇒ R₁(R₁ − 15) − 10(R₁ − 15) = 0
⇒ (R₁ − 15)(R₁ − 10) = 0
⇒ R₁ = 15 Ω or 10 Ω
Therefore, R₁ = 10 Ω, R₂ = 15 Ω
Related Questions
More WBBSE Hard level questions
The equivalent resistances of two conductors are 9 Ω and 2 Ω when they are connected in series and parallel combinations respectively. Find the resistances of those two conductors. OR Find the equivalent resistance between A and B points of the following circuit.
Two metallic wires A and B of the same length are made of the same material. The radius of wire A is double the radius of wire B. What is the ratio of resistances of the two wires? [3] OR There are three 220V-60W electric lamps and two 220V-100W electric fans in the house. The electric lamps are lit for 5 hours a day and the fans are run for 10 hours a day. If the cost per B.O.T unit is Rupees 5, what will be the cost of electricity for 30 days? [3]
If two electric bulbs of ratings ‘240V-60 W’ and ‘240V-100W’ are connected in series, which one will shine brighter? (Filaments of both the bulbs are of the same material).[3] OR An electric cell of internal resistance 5 Ω and emf 2 V is connected to a resistor of 15 Ω. Determine the potential difference between the two ends of the cell. [3]
The length of a wire having a resistance of 15 ohms is stretched by 20%. If the volume of the wire remains constant after stretching and its cross-section remains uniform throughout, determine the new resistance of the wire
Three equal resistors connected in series across a source of e.m.f. together dissipate 10 W of power. What would be the power dissipated if the same resistors were connected in parallel across the same source of e.m.f.?
Mention any two advantages of using alternating current over direct current. Why is hydroelectric power generation more environmentally friendly than thermal power generation? [1+2]
The cost per B.O.T unit of electrical energy is ₹6. Calculate the total cost of electricity used in a month of 30 days if ten 50 W bulbs are used for 10 hours daily. [3]
Write down the difference between dynamo and electric motor. What is earthing?
Write Faraday's laws of electromagnetic induction. Mention one advantage of using a LED lamp over an incandescent lamp. [2 + 1]
State Ohm's law. If a potential difference of 10 V is applied between the two ends of a conductor, an electric current of 0.1 A flows. Determine the resistance of the conductor. [2 + 1]
Which energy is transformed to which energy in an electric motor? Why in domestic circuits, electric bulbs, electric fans, refrigerators etc., are connected in parallel combination ? [1 + 2]
The total charge of how many electrons is equal to 1 coulomb? (a) 1.6 × 10¹⁹ (b) 6.25 × 10¹⁰ (c) 6.25 × 10¹⁸ (d) 6.023 × 10²³